The present invention relates to methods and apparatuses for determining reflectance characteristics of objects, more particularly for determining the bi-directional reflectance distribution function characteristic of a target surface.
The Bi-directional Reflectance Distribution Function (“BRDF”) is defined as the ratio of the differential scattered power to the differential incident power on a surface.                     BRDF        =                                            ⅆ                                                L                  s                                ⁡                                  (                                                            θ                      s                                        ,                                          ϕ                      s                                                        )                                                                    ⅆ                                                E                  i                                ⁡                                  (                                                            θ                      i                                        ,                                          ϕ                      i                                                        )                                                              =                                                                      P                  s                                /                Ω                            ⁢                                                           ⁢              A              ⁢                                                           ⁢              cos              ⁢                                                           ⁢                              θ                s                                                                    P                i                            /              A                                                          (        1        )            
The BRDF is typically measured using an apparatus which allows the sample to be illuminated with a collimated beam from a range of incident angles. A receiver, subtending a solid angle, can be positioned at a range of scatter directions. Alternatively, the relative radiance of the sample can be measured versus that of a standard characterized by a BRDF which is already known for the bi-directional geometry.
The U.S. Navy is interested in evaluating the BRDF of various types of coatings. The Coatings Engineering Evaluation Program (“CREEP”) is a conventional computer model for computing the BRDF of a coating having plural layers (e.g., a multilayered paint coating). A CREEP code can compute the scattering by pigments and rough interfaces as well as the multiple reflections between layers. Generally, the energy is broken down by CREEP into a beam component (which is energy that has been attenuated but not scattered) and a diffuse component (which is energy that has been scattered at least once). Existing computer codes contained in CREEP have been used to calculate the BRDF of pigmented coatings having various particles of different sizes, shapes and densities embedded in a binder matrix. However, CREEP is limitedly useful in such applications, since CREEP calculations result only in qualitative answers.
The BRDFs of various target surfaces have been measured by the U.S. Navy using a SOC-200 bi-directional reflectometer manufactured by Surface Optics Corporation, 11555 Rancho Bernardo Road, San Diego, Calif., 92127, telephone number (858) 675-7404, fax number (858) 675-2028, website “Surface Optics Web,” http://www.surfaceoptics.com/. Such reflectometric devices and techniques are limited in terms of size of the sample. For instance, the standard sample size for a Surface Optics Corp. SOC-200 is a one-inch diameter. Oversized samples of up to one-foot diameter can be accommodated, provided special care is taken. A notable disadvantage of this methodology is that the making of a sample without loss of the original information is not a trivial process. Furthermore, there are problems with light source and instrumentation stability, thus yielding highly variable results for identical samples.